3 In a tempering process, glass plate, which is initially at a uniform temperature Ti , is cooled by suddenly reducing the temperature of both surfaces to Ts. The plate is 20 mm thick, and the glass has a thermal diffusivity of 6 107 m2 /s.

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?

Farmer a has a deep well and needs a lot of water for her animals and crops. her neighbor, farmer b, has a shallower well. he needs less water than farmer a because his farm is smaller. in years of drought, sometimes farmer b can't get any water from his wells. what can farmer b do to decrease the likelihood of his well running dry?

The stopwatch used by a student to measure velocity of a pulse in a slinky was of least count 0.1 second. he stops the stopwatch when a pulse has made 3 journeys from one end to the other of the slinky. he finds the seconds hand to be at 52nd division. calculate the correct time noted by him.